The European Union in the Arctic: A Pole Position? Bruges Regional Integration & Global Governance Papers 4/2012, December 2012

With temperatures in the Arctic rising at twice the pace of anywhere else in the world, the European Union (EU) decided in 2008 to begin formulating an overall Arctic policy tackling maritime, environmental, energy and transport challenges. This attempt to draft a comprehensive policy on a topic that the EU had rarely touched upon unavoidably ran up against other existing strategies from Arctic and non-Arctic states. Against this background, this paper examines whether the EU’s current Arctic policy is conducive to framing a strategy that is both correctly targeted and flexible enough to represent Europe’s interests. It shows that the EU’s approach can serve as an effective foreign policy tool to establish the Union’s legitimacy as an Arctic player. However, the EU’s Arctic policy is still underestimating its potential to find common grounds with the strategic partners Russia and China. A properly targeted Arctic policy could help influence Russia over the EU’s interests in the Northern Sea Route and strengthen cooperation with China in an endeavour to gain recognition as relevant Arctic players.

Relationship between deadbeat and pole-placement discrete-time PID controllers

This paper considers PID control in terms of its implementation by means of an ARMA plant model. Two controller actions are considered, namely pole placement and deadbeat, both being applied via a PID structure for the adaptive real-time control of an industrial level system. As well as looking at two controller types separately, a comparison is made between the forms and it is shown how, under certain circumstances, the two forms can be seen to be identical. It is shown how the pole-placement PID form does not in fact realise an action which is equivalent to the deadbeat controller, when all closed-loop poles are chosen to be at the origin of the z-plane.

An implicit pole-assignment self-tuning regulator

A new self-tuning implicit pole-assignment algorithm is presented which, through the use of a pole compression factor and different RLS model and control structures, overcomes stability and convergence problems encountered in previously available algorithms. Computational requirements of the technique are much reduced when compared to explicit pole-assignment schemes, whereas the inherent robustness of the strategy is retained.

A specific pole placement technique to minimise hardware requirements within a real time terrestrial and cable video echo canceller

The real time hardware architecture of a deterministic video echo canceller (deghoster) system is presented. The deghoster is capable of calculating all the multipath channel distortion characteristics from terrestrial and cable television in one single pass while performing real time video in-line ghost cancellation. The results from the actual system are also presented in this paper.

Robust pole assignment in linear state feedback

Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.

Robust pole assignment and optimal stability margins

A robust pole assignment by linear state feedback is achieved in state-space representation by selecting a feedback which minimises the conditioning of the assigned eigenvalues of the closed-loop system. It is shown here that when this conditioning is minimised, a lower bound on the stability margin in the frequency domain is maximised.

Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.